Otto,
Maybe the following will help you. Let n be a counter for the number of
iterations.
n=0; x = FixedPoint[ f, x, SameTest :> (n++;Abs[#2-#1]<somesmallnumber&)]
Now the value of n is the number of iterations. Note the SetDelayed in
SameTest.
Regards,
Fred Simons
Eindhoven University of Technology